↑

Properties

Label 274890f
Number of curves $4$
Conductor $274890$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve([1, 1, 0, -2150978, -2055951372]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 274890f have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 + T\)
\(5\)\(1 + T\)
\(7\)\(1\)
\(11\)\(1 + T\)
\(17\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 - 4 T + 13 T^{2}\) 1.13.ae
\(19\) \( 1 + 8 T + 19 T^{2}\) 1.19.i
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 274890f do not have complex multiplication.

Modular form 274890.2.a.f

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - q^{11} - q^{12} + 4 q^{13} + q^{15} + q^{16} - q^{17} - q^{18} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.

Elliptic curves in class 274890f

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
274890.f3 274890f1 \([1, 1, 0, -2150978, -2055951372]\) \(-9354997870579612441/10093752054144000\) \(-1187519835417987456000\) \([2]\) \(16588800\) \(2.7387\) \(\Gamma_0(N)\)-optimal
274890.f2 274890f2 \([1, 1, 0, -40668898, -99806728748]\) \(63229930193881628103961/26218934428500000\) \(3084631416578596500000\) \([2]\) \(33177600\) \(3.0853\)  
274890.f4 274890f3 \([1, 1, 0, 18028447, 37123358133]\) \(5508208700580085578359/8246033269590589440\) \(-970137568134063257026560\) \([2]\) \(49766400\) \(3.2880\)  
274890.f1 274890f4 \([1, 1, 0, -118450273, 372888305077]\) \(1562225332123379392365961/393363080510106009600\) \(46278773058933461923430400\) \([2]\) \(99532800\) \(3.6346\)